Reproduce “Orthogonal Discrepancy Kernels for Learning with Partial Physics” on OpenResearch

About this paper

Swapnil Manna, Timothy J. Rogers, Lawrence Bull

This work introduces orthogonal discrepancy kernels for Gaussian Process regression within a SINDy-based framework to constrain data-driven components from capturing dynamics already representable by a physics-informed dictionary. The approach enhances the interpretability of hybrid models and their robustness to incomplete physical knowledge, demonstrating improved parameter identification and predictive accuracy in simulated systems.

Key insights

• Orthogonality between the GP discrepancy and the physics-informed dictionary ensures the black-box component exclusively learns genuinely missing or unmodeled dynamics, promoting full utilization of the physics-based white-box.
• The method effectively balances the flexibility of data-driven models with the structure and interpretability provided by physics-based knowledge, making it robust to partial physical understanding.
• Preventing "greedy" black-box behavior significantly improves the interpretability of identified physical parameters, which can aid in scientific discovery by distinguishing true discrepancies from flexible model fits.

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